The Role of Context-Related Parameters in Adults’ Mental Computational Acts (El papel de los parámetros relacionados con el contexto en actos de cálculo mental en adultos)

Nirmala Naresh

Description

Abstract
Researchers who have carried out studies pertaining to mental computation and everyday mathematics point out that adults and children reason intuitively based upon experiences within specific contexts
they use invented strategies of their own to solve real-life problems. We draw upon research areas of mental computation and everyday mathematics to report on a study that investigated adults’ use of mental mathematics in everyday settings. In this paper, we report on one adult’s use of mental computation at work and highlight the role of context and context related parameters in his mental mathematical activities.
Resumen
Los investigadores que han realizado estudios relacionados con el cálculo mental y las matemáticas cotidianas señalan que los adultos y los niños razonan intuitivamente basándose en las experiencias de contextos específicos
usan estrategias inventadas por sí mismos para resolver problemas de la vida real. Nos basamos en las áreas de investigación del cálculo mental y las matemáticas cotidianas para informar sobre un estudio que investigó el uso que hacen los adultos de la matemática mental en el entorno cotidiano. En este artículo, informamos sobre el uso que hace un adulto del cálculo mental en su trabajo y destacamos el papel del contexto y de los parámetros relacionados con el contexto en sus actividades matemáticas mentales.

Sujets

• Ethnomathematics
• India
• Cálculo mental

Informations

• Publié par: erevistas
• Publié le: 01 janvier 2012
• Nombre de lectures: 9
• Langue: Español

Extrait

THE ROLE OF CONTEXT-RELATED
PARAMETERS IN ADULTS’ MENTAL
COMPUTATIONAL ACTS
Nirmala Naresh and Norma Presmeg
Researchers who have carried out studies pertaining to mental computa-
tion and everyday mathematics point out that adults and children reason
intuitively based upon experiences within specific contexts; they use in-
vented strategies of their own to solve real-life problems. We draw upon
research areas of mental computation and everyday mathematics to re-
port on a study that investigated adults’ use of mental mathematics in
everyday settings. In this paper, we report on one adult’s use of mental
computation at work and highlight the role of context and context related
parameters in his mental mathematical activities.
Keywords: Adults’ mental mathematics; Ethnomathematics; India; Mental
computation; Workplace mathematics
El papel de los parámetros relacionados con el contexto en actos de
cálculo mental en adultos
Los investigadores que han realizado estudios relacionados con el
cálculo mental y las matemáticas cotidianas señalan que los adultos y
los niños razonan intuitivamente basándose en las experiencias de con-
textos específicos; usan estrategias inventadas por sí mismos para resol-
ver problemas de la vida real. Nos basamos en las áreas de investiga-
ción del cálculo mental y las matemáticas cotidianas para informar
sobre un estudio que investigó el uso que hacen los adultos de la mate-
mática mental en el entorno cotidiano. En este artículo, informamos so-
bre el uso que hace un adulto del cálculo mental en su trabajo y desta-
camos el papel del contexto y de los parámetros relacionados con el
contexto en sus actividades matemáticas mentales.
Términos clave: Cálculo mental; Etnomatemáticas; India; Matemática mental en
adultos; Matemáticas del trabajo
Naresh, N., & Presmeg, N. (2012). The role of context-related parameters in adults’ mental
computational acts. PNA, 6(2), 51-60. HANDLE: http://hdl.handle.net/10481/18315
52 N. Naresh and N. Presmeg
Mental computation, the process of carrying out arithmetic calculations without
the aid of external devices, is an indispensable tool that helps both adults and
children estimate and compute quickly and reasonably (Reys & Barger, 1994, p.
31). Researchers argue that people compute more efficiently mentally when
problems are embedded in a certain context than when posed as a plain computa-
tional problem, and they have called for investigation of everyday practices that
involve mental mathematics (Carraher, Carraher, & Schliemann, 1987; Saxe,
1991).
In the last two decades several researchers have analyzed and documented
the mathematical practices of adults as well as children, which take place outside
the school settings (e.g., Carraher, et al., 1987; D’Ambrosio, 1985; Gerdes, 1996;
Saxe, 1991). Although the past two decades have seen a surge in research dealing
with the everyday mathematical practices of adults, many of these studies were
conducted in the western hemisphere and developed nations of the world. Very
few studies have investigated the nature of workplace mathematics in developing
nations. We devised and completed a research study that attempted to fill in part
of this gap. The research reported in this paper is part of a larger project that in-
vestigated bus conductors’ use of mental computation in everyday settings in
Chennai, India. In this paper, we examine one bus conductor’s mental computa-
tional acts as he solved mathematics tasks at work and outside work settings.
THEORETICAL BACKGROUND
One can adopt two different approaches with respect to mental computation, tra-
ditional and contemporary views. According to the traditional view, mental com-
putation is considered a skill that only a few individuals possess and that is avail-
able to them. The contemporary view associates mental computation with higher
order thinking processes. According to this view, mental computation is consid-
ered a vehicle for promoting thinking, conjecturing, and generalizing based on
conceptual understanding rather than as a set of skills (Trafton, 1986). We adopt
the latter view. A traditional information-processing perspective has been signifi-
cantly used in research involving mental computation. This perspective involves
two assumptions, decomposition and decontextualization (Silver, 1994). Decom-
position implies that competence or skill can be broken down into individual el-
ements of skill or knowledge. Decontextualization implies that knowledge exists
in the mind of the individual and is independent of the situation in which it is
used. This theory has been criticized mainly because research evidence (e.g.,
Carraher, et al., 1987) suggests that, contrary to the view that an individual pos-
sesses a set of skills and competencies that can be decontextualized, research par-
ticipants were able to apply these in certain everyday situations and not in certain
school settings. Thus, researchers have argued that it would be worth considering
researching mental computation from an alternate perspective, one that would
PNA 6(2) The Role of Context-Related… 53
take into consideration the influence of context and context related parameters on
an individual’s use of mental computation (Reys & Barger, 1994; Silver, 1994).
The main assumption underlying our study is that adults’ mental computa-
tional activities in everyday situations—in particular, at work—are influenced by
context-related parameters. Hence, we needed a theoretical framework that
acknowledged the influence of context on their mathematical practices. We
chose Saxe’s four-parameter model (1991) to explore the overall research pur-
poses of this study. This model helped us bring out the context related parameters
that influenced bus conductors’ mathematical goals related to their work activi-
ties. In this paper, we will zoom in on one bus conductor’s mental mathematical
activities as he completed work-related and non work-related tasks. In particular,
we claim that context and context related parameters were crucial in this partici-
pant’s successful adaptation and application of mental computational strategies
in everyday situations. Thus, the question investigated is as follows: What role
do context and related parameters play in one bus conductor’s mental mathemat-
ics activities?
METHODOLOGY
The overall research study was qualitative in nature. An instrumental case study
approach was used to select participants for this study. The bus conductors are
employees of the government organization, Metropolitan Transport Corporation
(MTC). After gaining entry into the organization, the first author used conven-
ience sampling to choose a bus depot for investigation. Purposive sampling was
used to select the five participants, who were carefully and appropriately chosen
based on their years of service with the MTC, educational qualifications, service
records, and their willingness to participate in the study. In this paper, we focus
on data pertaining to one bus conductor, Vira (pseudonym) chosen because of
salient elements in his case study.
Data collected for this study include official documents, field notes, sum-
mary of observations and informal conversations, transcriptions of formal and
semi structured interviews and personal reflections. The primary researcher (PR)
accompanied and observed Vira during his work shift three times a week, ob-
serving a total of ten trips. Based on the first few observations, the PR singled
out several episodes that were most helpful in examining Vira’s use of mental
computation at work. Snippets of Vira’s work-related activities were isolated and
used to describe his work-related mathematical activities. For further analysis,
we scrutinized his work-related mathematical activities, and identified and de-
scribed solution strategies he used to complete these activities.
In order to investigate the influence of context-related parameters on Vira’s
mental computational activities, he was asked to solve two types of computation-
al tasks outside work settings, contextual (CT) and plain (PT). The PR adminis-
PNA 6(2) 54 N. Naresh and N. Presmeg
tered these tasks orally in an informal setting and Vira was given 10-15 seconds
to complete each task. The CTs were administered first; the PTs were adminis-
tered a week later in the same setting. The PTs involved the same mathematical
computation as the CTs, but were completely stripped of the context. We com-
pared Vira’s performances on CTs and PTs to investigate the influence of context
on his computational skills.
ANALYSIS AND RESULTS
In this section, first we present data that demonstrate Vira’s use of mental com-
putation connected to his work-related activities. Elsewhere we have documented
in detail, mental mathematical methods bus conductors used to complete ticket
transactions (Naresh & Presmeg, 2008).
Mental Computation-Work Setting
At work, Vira used mental computation (a) to complete ticket transactions, (b) to
determine the overall ticket sales amount, and (c) to determine his everyday al-
lowance (batta). In this paper, we will highli